Rendered image in eevee is not displaying shadows
EEVEE fakes pretty much everything in the scene when rendering. This includes Ambient Occlusion (which creates more realistic shading in EEVEE), reflections, refractions, etc. If you want a better result in EEVEE, I would recommend you use an HDRI map, and enable the checkbox for &quot;Ambient Occlusion&quot; in the render properties panel.
You can download high quality HDRs and HDRIs for free here.
More about Ambient Occlusion (AO) in the Blender Manual here.